Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-3y &= -4 \\ -6x-2y &= -3\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-6x = 2y-3$ Divide both sides by $-6$ to isolate $x$ $x = {-\dfrac{1}{3}y + \dfrac{1}{2}}$ Substitute this expression for $x$ in the first equation. $-5({-\dfrac{1}{3}y + \dfrac{1}{2}}) - 3y = -4$ $\dfrac{5}{3}y - \dfrac{5}{2} - 3y = -4$ Simplify by combining terms, then solve for $y$ $-\dfrac{4}{3}y - \dfrac{5}{2} = -4$ $-\dfrac{4}{3}y = -\dfrac{3}{2}$ $y = \dfrac{9}{8}$ Substitute $\dfrac{9}{8}$ for $y$ in the top equation. $-5x-3( \dfrac{9}{8}) = -4$ $-5x-\dfrac{27}{8} = -4$ $-5x = -\dfrac{5}{8}$ $x = \dfrac{1}{8}$ The solution is $\enspace x = \dfrac{1}{8}, \enspace y = \dfrac{9}{8}$.